01_PRB_Kumpf

8/8/2019 01_PRB_Kumpf

1/10

Structure of metal-rich 001 surfaces of III-V compound semiconductors

C. Kumpf,* D. Smilgies, E. Landemark, M. Nielsen, and R. FeidenhanslMaterials Research Department, Riso National Laboratory, DK-4000 Roskilde, Denmark

O. Bunk, J. H. Zeysing, Y. Su, and R. L. Johnson II. Institut fur Experimentalphysik, Universitat Hamburg, D-22761 Hamburg, Germany

L. Cao and J. ZegenhagenEuropean Synchrotron Radiation Facility, Bote Postale 220, F-38043 Grenoble Cedex, France

B. O. FimlandDepartment of Physical Electronics, Norwegian University of Science and Technology, N-7491 Trondheim, Norway

L. D. MarksDepartment of Material Science and Engineering, Northwestern University, Evanston, Illinois 60208

D. EllisDepartment of Chemistry, Northwestern University, Evanston, Illinois 60208

Received 22 February 2001; published 17 July 2001

The atomic structure of the group-III-rich surface of III-V semiconductor compounds has been under intense

debate for many years, yet none of the models agrees with the experimental data available. Here we present amodel for the three-dimensional structure of the (001)-c(82) reconstruction on InSb, InAs, and GaAssurfaces based on surface x-ray diffraction data that was analyzed by direct methods and subsequent leastsquares refinement. Contrary to common belief the main building blocks of the structure are notdimers on thesurface but subsurface dimers in the second bilayer. This essential feature of the structure is accompanied bylinear arrays of atoms on nonbulklike sites at the surface which, depending on the compounds, exhibit a certaindegree of disorder. A tendency to group-III-dimer formation within these chains increases when descending theperiodic table. We propose that all the c(82) reconstructions of III-V semiconductor surfaces contain thesame essential building blocks.

DOI: 10.1103/PhysRevB.64.075307 PACS numbers: 68.35.Bs, 61.10.i, 81.05.t

I. INTRODUCTION

Within the last decade III-V compound semiconductorshave become extremely relevant for fabricating high-speedelectronic and optoelectronic devices. Layer growth and ep-itaxial behavior, which are strongly influenced by the mor-phology of the substrate surface, play an important role forthe fabrication process. Thus, detailed knowledge about thegeometric structure of the surface is essential. Depending onpreparation, temperature, and especially whether group-III-or group-V-rich conditions are dominant, the 001 surfacesof III-V compound semiconductors show a wealth of differ-ent surface reconstructions. For the group-V-rich surfaces,group-V dimers have been clearly identified as the basicbuilding blocks in these reconstructions. McConville and co-workers saw Sb-Sb dimers on the InSb(001)-c(44) sur-face in scanning tunneling microscopy STM images1

whereas Gothelid et al. found As dimers in theInAs(001)-2-(24) structure using surface x-ray diffrac-tion SXRD.2 These surface structures were strongly sup-ported recently by density-functional theory and first-principles electronic structure calculations.3,4 It has also beengenerally believed that the group-III-rich surface consists ofgroup-III dimers,5 but no agreement on a specific modelexists in the literature. In an early publication, based on high-

resolution photoelectron spectroscopy PES, John and co-workers proposed an InSb--c(82) model consisting ofsix In-In dimers, three within each (42) subcell.6 Figure1a illustrates this so-called missing-dimer model. Thismodel was supported for InSb and GaAs by various experi-mental methods, most frequently STM and low-energy elec-tron diffraction LEED.1,7 However, it was also questioned,e.g., by Varekamp et al. in a STM study on InSb.8 Biegelsenet al. modified the model by suggesting only two dimers inthe top layer and one in the second bilayer9 see Fig. 1b.This so-called 2 model was proposed on the basis of aSTM study on the GaAs surface, and was supported later byboth experimental10 and theoretical studies.11 Another vari-ant, the 3 model for InAs see Fig. 1c, was suggested byOhkouchi and Ikoma.12 It contains one top-layer and twosecond-bilayer dimers and was favored by a combinedLEED and STM study.13 All these models have a commonfeature: Group-III surface dimers are the primary structuralelement. However, the features in the STM images inter-preted as dimers have never been uniquely identified as re-ally being made up of two atoms, as in the case of group-V-rich surfaces. Furthermore, most of the STM measurementssuggested a (41) or (42) unit cell1,10,12,14 whereas alldiffraction experiments clearly showed a c(82) structure.This was attributed to defects13 and often a coexistence of

PHYSICAL REVIEW B, VOLUME 64, 075307

0163-1829/2001/647/07530710 /$20.00 2001 The American Physical Societ64 075307-1

8/8/2019 01_PRB_Kumpf

2/10

(42) and c(82) reconstructed regions was assumed.1,8,13

In more recent STM work on InSb additional weak featuresindicating the c(82) unit cell were found.8,15

Skala and co-workers modified the group-III-dimer modelsuggesting additionally group-V dimers on top of doublerows of group-III atoms,16 a model again based on STMmeasurements on GaAs see Fig. 1d. Five years later thismodel was seized again in a SXRD study on InSb by Jonesand co-workers.17 They replaced the group-V dimers bysingle group-III atoms forming chains along the 110 axiswhich are separated from each other by group-V dimers seeFig. 1e. Their model contains no group-III dimers and was

supported by a reinterpretation of STM images.15 Recently acompletely different model was proposed independently bytwo groups; theoretical total-energy calculations combinedwith a LEED analysis18 by one group and direct methodsapplied to SXRD data by the other.19 The present article is anextension of the latter work. Characteristic features of thismodel are subsurface dimerization of group-III atoms in thesecond bilayer and linear arrangements of atoms at the sur-

face. The subsurface dimerization is the only attribute pro-ducing a c(82) periodicity and explains the contradictionbetween the (42) unit cell observed in STM and the c(82) diffraction patterns. Group-III dimers in the top layerare present on GaAs but not on the heavier III-V compoundsInAs and InSb.

A fundamental problem with structure determination is toidentify the correct solution; when refining a structure it israrely clear whether a local or the global minimum of thegoodness-of-fit function has been found. For bulk structuredetermination using x-ray diffraction data, this ambiguity hasbeen largely removed using what are called direct methods.20

Direct methods find probable values for the phases of the

measured reflections, consistent with the fact that the scatter-ing arises from atoms. Combining these phases with themeasured amplitudes allows approximate maps of the chargedensity to be calculated. Placing atoms at the peaks in thesemaps gives a first approximation to the structure, and willalmost always yield a fairly good fit to the data. In manycases not all atoms appear at first, but by using Fourier dif-ference methods the rest of the structure can be found with-out much difficulty. The power of direct methods is that theyeliminate the need to guess a model for the structure; theyyield a set of plausible structures against which subsequentrefinements are carried out. While direct methods have beenused successfully on two-dimensional in-plane SXRD data

or transmission electron surface diffraction data,

21

extendingthem to three-dimensional SXRD data is not simple. Onereason for this is that large out-of-plane data sets are neces-sary for finding stable solutions with a three-dimensional di-rect methods code. But since it is often too timeconsumingeven at modern synchrotron-light sourcestoobtain a full-size out-of-plane data set it is common to mea-sure a fairly complete two-dimensional data set typically80% of the available reflections and only a rather limitednumber of fractional-order rods. The small number of three-dimensional measurements makes it harder to obtain stablesolutions. We have recently shown that the mathematical ap-proach of feasible sets22 developed for image restorationproblems can be applied to crystallographic problems,23 per-

mitting additional constraints to be introduced that enablefull, ab initio, surface structure determination to be per-formed in three dimensions.24 Since this is a truly model-independent approach, group-III dimers will only arise in thedata analysis if they are an intrinsic part of the structure.

II. EXPERIMENT

Several data sets on 001 surfaces of three types of III-Vsemiconductor, GaAs, InAs, and InSb, were measured. InSband InAs samples were prepared in an ultrahigh vacuum

FIG. 1. Popular models from the literature for the c(82) re-constructed In-rich 001 surface of InSb: a model missing-dimer model of John et al. Ref. 6 1989, b 2 model of Bie-gelsen et al. Ref. 9 1990, c 3 model of Ohkouchi and IkomaRef. 12 1994, d model of Skala et al. Ref. 16 1993, and emodel of Jones et al. Ref. 17 1998.

C. KUMPF et al. PHYSICAL REVIEW B 64 075307

075307-2

8/8/2019 01_PRB_Kumpf

3/10

UHV system using the standard surface preparation tech-nique of repeated cycles of argon-ion bombardment and an-nealing at the appropriate temperature. GaAs surfaces wereprepared by using GaAs001 wafers, the surfaces of whichhad been grown by molecular beam epitaxy MBE andwhich had been covered by a protective layer of amorphousarsenic immediately after the growth. Before the SXRD mea-surements, the cap layer was desorbed in UHV at 450C.Subsequent annealing for 5 min at 490C yielded aGaAs(001)-c(82) reconstruction as confirmed by LEED.Scanning tunneling microscopy was used to ensure that theGaAs001 surfaces used for the SXRD measurements werewell ordered and uniformly c(82) reconstructed. Figure 9below shows a representative STM image from theGaAs001 surface. More STM images from MBE-grownGaAs001 surfaces prepared by thermal desorption of an Ascapping layer are presented in Ref. 25 and they are similar tothe images from samples prepared using other techniques.6,14

After preparation the samples were transferred to a smallportable UHV chamber which was mounted on the z-axis

diffractometer on the BW2 wiggler beamline at the Ham-burger Synchrotronstrahlungslabor HASYLAB and alignedwith respect to the incident x-ray beam. The glancing anglewas 0.6, 0.5, and 0.2 for the measurements on InSb,GaAs, and InAs, respectively. On all samples extended in-plane and out-of-plane data sets were measured at wave-lengths between 1.24 and 1.42 . The intensity of eachreflection was determined by rotating the sample about itssurface normal ( scans. The peaks were integrated, back-ground subtracted, and corrected in the standard manner forLorentz and polarization factors, active sample area, and rodintercept.26 The 001 surface of the zinc-blende structure has

FIG. 2. Experimental Patterson map calculated from our mea-

sured in-plane data set a and theoretical Patterson maps calculatedfrom our model b and from different models from literature: c2 model of Biegelsen et al., Ref. 9, d model of Skala et al.Ref. 16, and e model of Jones et al. Ref. 17.

FIG. 3. a Contour map of the charge density distribution in thex-y plane obtained from the two-dimensional direct method code,using in-plane data only. Each maximum corresponds to the posi-tion of an atom in the uppermost layer. One c(82) unit cell isshown with the origin located at the lower left. b Two-dimensionalsections of the three-dimensional map showing contours of thecharge density in x-y planes at different heights z. Numbers in theleft margin indicate the z coordinate in ; z0 corresponds to theheight of the uppermost In atoms on an unreconstructed In-terminated surface. In the second bilayer the dimers are marked Dand lines between the atoms are drawn to guide the eye.

STRUCTURE OF METAL-RICH 001 SURFACES OF . . . PHYSICAL REVIEW B 64 075307

075307-3

8/8/2019 01_PRB_Kumpf

4/10

only twofold rotational symmetry; thus there is only one ro-tational domain. By averaging equivalent reflections using ac2mm symmetry systematic errors in F2 of 7.8%,7.2%, and 10.2% were determined for the in-plane data setsof InSb, GaAs, and InAs, respectively. The final data setsconsisted of 171, 112, and 75 nonequivalent in-plane reflec-tions, 14, 17, and 18 fractional-order rods with 282, 548, and566 reflections as well as three, two, and five crystal trunca-tion rods CTRs with 137, 71, and 375 reflections InSb,GaAs, and InAs, respectively. On the InSb data set a (00l)rod was measured as well 95 reflections but not included inthe refined data set for reasons discussed below. The eighth-

order reflections from InAs were so broad that their inte-grated intensities could not be evaluated, so the InAs in-plane data set consisted only of reflections from the (41)subcell. Standard LEED coordinates ( a(1/2)110bulk , b(1/2)110bulk , c001bulk are used in the following.

III. DATA ANALYSIS AND RESULTS

A. Patterson function

For solving surface structures considerable insight can begained from a contour plot of the Patterson function

Px,y h ,k

Fhk02cos2 hxky 1

where Fhk02 is the measured intensity of the in-plane re-

flections (hk0). The experimental Patterson map calcu-lated from the InSb data is shown in Fig. 2a. Each positivepeak in the map corresponds to an interatomic distance vec-tor in the unit cell projected onto the surface plane. Severalclearly separated peaks can be seen in the irreducible unit. Asa first test for the correctness of a specific model we cancompare the experimental Patterson map of Fig. 2a with atheoretical Patterson map calculated on the basis of themodel. Equation 1 gives the theoretical Patterson functionif the measured structure factors are replaced by those calcu-lated from the model, using the same subset of ( hk0) reflec-tions. In Fig. 2b a contour plot of such a theoretical Patter-son function is shown for the model presented in this work.Comparison with a reveals excellent agreement betweenthe experimental and theoretical Patterson maps. Figures2c e are theoretical Patterson maps for the most popularmodels from the literature. The arrows on the left axis of thefigure mark a peak at 0,0.55 arising from the dimer dis-tance in the Biegelsen and Skala models. This peak is also

FIG. 4. InSb data set. Upper left: Plot of the in-plane data. The areas of the filled and open semicircles represent measured and calculatedintensities, respectively. Gray/white circles have been scaled by a factor of 0.5. Upper right: integer-order rods. Bottom: fractional-order rods.


075307-4

8/8/2019 01_PRB_Kumpf

5/10

present in the theoretical Patterson maps of the models byJohn et al. and Ohkouchi and Ikoma not shown. The ab-sence of the peak in the experimental Patterson function isclear evidence that surface dimers in the y direction i.e.,group-III dimers are not present in this reconstruction. Othersignificant differences between experimental and theoreticalPatterson maps occur at 1.7,0 and 2.3,0, where relatively

strong peaks in the experimental Patterson plot are not repro-duced in the theoretical plots Figs. 2c e. Some other fea-tures are reflected quite well by the Jones model, e.g., thepeaks at approx 2,0.25, 2,0.75, and 0.5,0.5, even thoughthey are weaker in the experimental Patterson plot. In sum-mary, judging from the Patterson maps, the Jones model hassome correct features, but other models containing group-IIIdimers as the basic building block can be eliminated.

B. Direct methods

To find a starting model for the refinement of our data wedid not try to modify models from the literature but useddirect methods. We first analyzed the InSb surface, a reason-ably complete c(82) data set, using both the two- and thethree-dimensional direct method code. We found a solutionto the structure relatively straightforwardly in two dimen-sions Fig. 3a and in three Fig. 3b. In both cases thesolution was unambiguous and placing atoms at the peaks inthe maps gave relatively low R factors confirming that thedata set used is of high quality. Contrary to the models fromliterature described above we found an indium dimer only inthe second bilayer, not in the top layer. The upper layer con-tains rows of In atoms along b and, with only a small occu-pancy, an indium dimer site In2d, see Fig. 5 below within

these rows. Since the two types of atom in InSb as well as inGaAs have almost the same number of electrons it was stillunclear at this point in the data analysis which type of atomoccupies which site. But the InAs data allowed this questionto be answered, as will be discussed below. The second fairlycomplete data set is that of GaAs. The result of two-dimensional 2D direct methods showed the same basic el-

ements as for InSb except that the sites corresponding to In1and In2 were absent and the In2 d dimer site had a higheroccupancy. The three-dimensional solutions were just aboutstable, indicating the same structure we found for InSb, butwith different occupancies. Because of missing eighth-orderreflections the last data set, InAs, did not yield a solution inthree-dimensional direct methods, although the two-dimensional results were similar to those for GaAs and InSb.In conclusion, the direct methods yielded one commonmodel for InSb and GaAs, which was used as a startingmodel for refinement with a least-squares algorithm.

C. Refinement

We first discuss the result of the refinements for the InSbdata set. Refining the positions of the uppermost three InSbbilayers and the occupancy for the sites In1 and In2d thoseshowing a reduced occupancy in direct methods results in

23.95 for the whole data set and indicates that the model

found in direct methods is basically correct. This first fit wasclose to the starting model, i.e., to the direct methods result,and could not be improved significantly by refining the oc-cupancies of other atoms within the top bilayer. Note that thestarting model based on direct methods was derived fromfractional-order data only. However, the model was immedi-

FIG. 5. Color Structural model for InSb viewed from above a and from the side b. In and Sb atoms are shown as red and blue circles.In dimers are colored green. Atoms in deeper layers are indicated by pale colors. The main atoms are labeled and the dimer site In2 d isshown at only one location. All gray bars represent covalent In-Sb bonds; other bonds are indicated schematically.


075307-5

8/8/2019 01_PRB_Kumpf

6/10

ately able to fit the CTRs as well, which provides additionalevidence for its correctness. The best fit depicted in Fig. 4with 22.40 was achieved by including the atomic posi-tions of two more bilayers in the refinement and allowing theisotropic Debye-Waller DW factors for all atoms in thetwo uppermost bilayers to be adjusted. The topmost layers ofthe corresponding structural model are shown in Fig. 5.Deeper layers showed only very small deviations from bulkpositions. The atomic parameters are listed in Table I. In Fig.6 we present the experimental data for the InSb (00 l) rodand a calculation based on our model solid line. If we in-

clude this rod in our data set 2 increases to 3.49; furtherrefinement of the model brings 2 down to 3.15 which is stillsignificantly worse than the value of 2.40 obtained for thedata set without the (00l) rod. It should be noted that ingeneral the (00l) rod is hard to fit, since everything on thesurface including unreconstructed areas and inhomogeneitiescontributes to it. Hence we left out the (00l) rod in the quan-titative analysis of the surface structure.

The refinement of the GaAs data set was as straightfor-ward as for InSb and the same basic model was employed,but with different DW factors and occupancy of some atomic

TABLE I. Atomic parameters for the ( 001)c(82) reconstruction of InSb, GaAs, and InAs. Positions are given in LEED coordinates,Debye Waller DW factors in 2. All DW factors are isotropic, except for atoms at site 1 in the InAs structure, which shows a large in-planedisorder. DW factors not listed in the table were fixed at bulk values: DW(In)1.60 2, DW(Ga)1.43 2, DW(Sb)1.25 2, andDW(As)0.87 2. Standard deviations are calculated assuming uncorrelated parameters. Values listed without errors were not refined dueto c2mm symmetry constraints.

Site InSb: position; DW (2) GaAs: position; DW (2) InAs: position; DW (2)

1 In/Ga 2.000, 0.500, 0.051(4); 8.6 5 2.000, 0.500, 0.0774; 1.8 4 2.000, 0.500, 0.0041;a

2 In/Ga 0.000, 1.000, 0.295(4); 7.3 4 not occupied 0.000, 1.000, 0.251(1) ; 3.14132d In/Ga 0.000, 0.7306, 0.208(7); 7.2 8 0.000, 0.7072, 0.275(1); 2.8 2 not occupied3 In/Ga 0.000, 0.000, 0.203(3); 6.4 3 not occupied 0.000, 0.000, 0.101(1) ; 6.57174 In/Ga 0.8811, 0.000, 0.159(2) ; 1.5810 0.8701, 0.000, 0.171(1) ; 2.609 0.9021, 0.000, 0.166(1) ; 5.46115 In/Ga 0.8841, 1.000, 0.162(2) ; 1.5810 0.8831, 1.000, 0.179(1) ; 1.548 0.9231, 1.000, 0.108(1) ; 0.2366 Sb/As 0.5321, 0.5111, 0.106(1) ; 1.778 0.5401, 0.5111, 0.111(1) ; 1.184 0.5631, 0.4823, 0.089(1) ; 2.6767 Sb/As 1.4851, 0.000, 0.220(2) ; 1.4911 1.4611, 0.000, 0.241(1) ; 0.586 1.5291, 0.000, 0.238(1) ; 2.32158 Sb/As 1.4931, 1.000, 0.255(2) ; 1.6712 1.4741, 1.000, 0.235(1) ; 1.458 1.4741, 1.000, 0.251(1) ; 1.93129 In/Ga 0.5161, 0.3151, 0.536(2) ; 2.337 0.5261, 0.3301, 0.538(1) ; 2.036 0.5190, 0.3341, 0.511(0) ; 1.98 510 In/Ga 1.4831, 0.5001, 0.490(1) ; 1.767 1.4841, 0.5301, 0.494(1) ; 1.145 1.4980, 0.4893, 0.502(0); 1.76511 Sb/As 0.000, 0.4951, 0.730(1) ; 0.798 0.000, 0.4921, 0.742(1) ; 0.375 0.000, 0.5004, 0.733(1) ; 1.23812 Sb/As 1.0081, 0.4941, 0.750(1) ; 1.296 1.0130, 0.4981, 0.769(0) ; 0.454 1.0010, 0.5004, 0.757(1) ; 1.507

13 Sb/As 2.000, 0.500,

0.720(1) ; 1.028 2.000, 0.500,

0.730(1) ; 0.375 2.000, 0.500,

0.751(1) ; 1.768In/Ga 0.000, 0.000, 1.007(2) 0.000, 0.000, 0.992(1) 0.000, 0.000, 0.970(1)In/Ga 1.0261, 0.000, 0.999(1) 1.0171, 0.000, 1.025(1) 1.0021, 0.000, 1.011(1)In/Ga 1.9961, 1.000, 0.975(1) 1.9941, 1.000, 0.982(1) 1.9952, 1.000, 1.000(0)In/Ga 0.9871, 1.000, 1.002(2) 1.0001, 1.000, 0.999(1) 1.0121, 1.000, 0.991(1)In/Ga 0.000, 1.000, 0.972(2) 0.000, 1.000, 1.011(1) 0.000, 1.000, 0.992(1)Sb/As 0.5081, 0.000, 1.253(1) 3.5051, 0.000, 1.256(1) 0.5151, 0.000, 1.248(1)Sb/As 1.5261, 0.000, 1.251(2) 1.5241, 0.000, 1.252(1) 1.5031, 0.000, 1.234(1)Sb/As 1.5021, 1.000, 1.249(2) 1.5091, 1.000, 1.253(1) 1.5051, 1.000, 1.270(1)Sb/As 0.4911, 1.000, 1.246(1) 0.4951, 1.000, 1.249(1) 0.4741, 1.000, 1.245(1)In/Ga 0.4981, 0.4941, 1.500(1) 0.4971, 0.5111, 1.502(1) 0.4950, 0.5162, 1.493(0)In/Ga 1.5091, 0.5011, 1.498(1) 1.5091, 0.4801, 1.500(1) 1.5030, 0.4651, 1.502(0)Sb/As 2.000, 0.500, 1.748(1) 2.000, 0.500, 1.756(1) 2.000, 0.500, 1.754(1)

Sb/As 1.0031, 0.5031, 1.742(1) 1.0010, 0.5061, 1.747(0) 0.9970, 0.4825, 1.747(1)Sb/As 0.000, 0.4991, 1.744(1) 0.000, 0.4961, 1.753(1) 0.000, 0.5004, 1.750(1)In/Ga 1.9961, 0.000, 2.003(1) 1.9961, 0.000, 2.003(1) 2.0002, 0.000, 2.004(0)In/Ga 1.0001, 1.000, 1.997(2) 1.0011, 1.000, 1.998(1) 0.9941, 1.000, 2.004(1)In/Ga 1.0011, 0.000, 1.990(1) 1.0011, 0.000, 1.995(1) 1.0001, 0.000, 1.991(1)In/Ga 0.000, 1.000, 1.993(2) 0.000, 1.000, 1.999(1) 0.000, 1.000, 1.998(1)In/Ga 0.000, 0.000, 2.004(2) 0.000, 0.000, 2.002(1) 0.000, 0.000, 1.998(1)Sb/As 1.5001, 1.000, 2.250(2) 1.5001, 1.000, 2.250(1) 1.5001, 1.000, 2.250(1)Sb/As 1.5001, 0.000, 2.250(2) 1.5001, 0.000, 2.250(1) 1.5001, 0.000, 2.250(1)Sb/As 0.5001, 1.000, 2.250(1) 0.5001, 1.000, 2.250(1) 0.5001, 1.000, 2.250(1)Sb/As 0.5001, 0.000, 2.250(1) 0.5001, 0.000, 2.250(1) 0.5001, 0.000, 2.250(1)

aThis site has anisotropic DW factors: DWx4.3(1) 2, DWy200

2 not refined, and DWz5.5(3) 2.


075307-6

8/8/2019 01_PRB_Kumpf

7/10

sites. Several tests were carried out to evaluate the occupan-cies for all top-layer atoms. As a result the sites In2 and In3are not occupied in this structure and the site In1 has a re-duced occupancy of 19%. However, unlike in the InSb struc-ture, the dimer site In2d is occupied to 63% see Table II.The first fitpositions of three layers and occupancies of In1and In2d were refinedyielded 23.32 and could be im-proved to 22.18 by including more bulk layers and DWfactors. Fractional- and integer-order rods for this fit areshown as solid lines in Fig. 7. The model is only slightlydifferent from the one proposed on the basis of theoreticalconsiderations by Lee et al.18 The main differences are theoccupancies of sites In1 and In2 d, which are fixed to 0%and 100% in their model see also Table II. The dotted linesin Fig. 7 correspond to a fit with this constraint. Only smalldifferences can be seen between the two fits in the figure;

however, the difference in the goodness of fit is significant(23.14 when fitting the Lee model to our data.

Refining the InAs data was more problematic because ofambiguity in the position of the In1 site due, in part, to themissing eighth-order reflections. No good fit could beachieved by refining only three bilayers Even a fit with theset of parameters that gave the best fits for InSb andGaAspositions of five bilayers, isotropic DW factors fortwo bilayers, and occupancies for the critical sites In13

resulted in 211.2. Satisfactory fits could only be achievedby introducing anisotropic DW factors for site In1 with alarge y component. This indicates disorder along the110bulk direction at this site and explains the diffuse eighth-order reflections. As a consequence it was difficult to findexact values for the occupancies of the uppermost sites. Thebest fit we could achieve, with 70% occupancy for In2 and13% for In2d, yielded 22.55, but fixing these sites at

100% and 0%, respectively, did not increase 2 significantly(22.71; see Table II.

Since In and Sb have nearly the same number of electronsthey scatter x-rays almost equally strongly, as do Ga and As.From x-ray diffraction results on InSb or GaAs it is thereforedifficult to judge which site is occupied by group-III atomsand which by group V. But with the InAs data set it waspossible to determine the identity of the atoms. From priorknowledge about the orientation of the c(82) cell relativeto the bulk the atom type was clear for all sites except for theuppermost ones In15, Sb6 8. Despite the ambiguous re-sults from the InAs data set concerning the In1 site, the fit tothe InAs data set was sufficient to identify the atoms of all

sites with 100% occupancy, i.e., all sites except In13. Thedetermination was performed by replacing all top-layer at-oms In and As in the final InAs model with Nb which islocated halfway between In and As in the periodic table andcalculating the density difference map for this modeli.e.,the difference between the 2D electron density of the modeland the 2D electron density resulting from the measurement,neglecting differences in the phases:

x ,y ,0exptx,y ,0modelx ,y ,0

h ,k

Fhk0,exptFhk0,model

cos2 hxky hk0,

where hk0 is the phase of the structure factor Fhk0Fhk0exp(ihk0), calculated from the model. A contour plotof the differences is shown in Fig. 8. Each In As atomappears as a positive negative peak because its electrondensity is higher lower than that of Nb. It can clearly beseen that In atoms are located at site In4 0.9,0 and In50.9,1 and As at As1 0.5,0.5, As2 0,1.6, and As3 0,2.4.The atoms on sites In13 cannot be identified from this plotdue to their reduced occupancy. But from the bond lengths,STM images, and the fact that the surface is In rich it is mostlikely that they are indium.

IV. DISCUSSION

A unique model for the group-III-rich 001 surface ofIII-V compound semiconductors has been found, based onmeasurements on three different compounds InSb, GaAs,and InAs. The model is in excellent agreement with recentLEED measurements and density-functional theory.18 It issignificantly different from all previous models in a numberof features, most prominent of which is the subsurfacedimerization in the second bilayer site In9. The dimer dis-tances (2.89 for In-In in InSb, 2.64 for Ga-Ga in

FIG. 6. (00l) rod from the c(82) InSb001 surface datapoints with error bars and the curve calculated with our modelsolid line. Note the good agreement around the weak 002 reflec-tion shown in the inset. For comparison, calculations for a truncatedInSb crystal dashed line and the missing-dimer model Ref. 6dotted line are shown.

TABLE II. Comparison of the occupancies of the sites labeledIn1, In2, In2d, and In3 for the three different surfaces. For InAs andGaAs the results for two different fits are listed, with the corre-

sponding 2 values. Standard deviations are calculated assuminguncorrelated parameters. Values listed without errors were not re-fined.

In1 In2 In2d In3 2

InSb 57(1)% 72(2)% 28(1)% 100% 2.40InAs 100% 100% 0% 100% 2.71InAs 100% 68(7)% 13(4)% 100% 2.55GaAs 19(1)% 0% 63(1)% 0% 2.18GaAs Ref. 18 0% 0% 100% 0% 3.14


075307-7

8/8/2019 01_PRB_Kumpf

8/10

GaAs are in very good agreement with covalent bondlengths from literature (2.88 for In, 2.54 for Ga. Theordering of these subsurface dimers is the only distinct ele-ment with a c(82) periodicity. Apart from a very smalldifference in the z coordinate of the atoms in sites In2 andIn3 the top layer is (41) reconstructed. This explains whyit has been so difficult to see the c(82) periodicity in STMimages, whereas it was easily visible in diffraction patterns.A second important feature is the two chains in the 110bulkdirection formed by the atoms on sites In1 and In2,3. Theyare marked by a red and a green arrow in Fig. 5. In the model

of Jones et al. only one of these chains was present.17 Theseauthors used a relatively small data set without fractional-order out-of-plane data and with significantly higher statisti-cal errors evaluated from the errors given in their Table I.We tried to fit their model to our more complete data set butcould not achieve a 2 below 20; in particular, the fractional-order rods could not be fitted. The chains in our model areshifted relative to each other by (0,0.5) LEED , i.e., one quarterof the unit cell in the y direction, so they have a differentregistry with the substrate. The Sb atoms in the chain markedby the red arrow sites 7 and 8 are located at bulk positions,

FIG. 7. Integer- and fractional-order rods

from the GaAs data set: The error bars representmeasured intensities, the solid line is calculatedusing our best fit. The dotted line is calculatedusing a model Ref. 18 that differs from ours inthe occupancy of the sites 1 (0%) and 2d(100%) see Table II.


075307-8

8/8/2019 01_PRB_Kumpf

9/10

whereas the indium atoms site 1 are located on an addi-tional not bulklike site. The Sb atoms in the second chain

site 6, chain marked by a green arrow are shifted by(0,0.5)LEED relative to bulk positions, which explains thesubsurface dimerization. In a bulk-terminated crystal each Inatom in the second bilayer sites 9 and 10 would have twobonds to Sb atoms at the surface, as is the case for the atomson site In10 having bonds to Sb7 and Sb8. Analogously, theIn9 atoms would have bonds to two atoms on site Sb6, ifthey were on bulk sites. But since the entire chain containingthe Sb6 atoms is shifted by (0,0.5) LEED one of the In9-Sb6bonds is broken, and a dimer bond between neighboring In9atoms is formed instead. Atomic distances within both chainsIn2-Sb6, In3-Sb6, In1-Sb7, and In1-Sb8 are between3.44 and 3.53 indicating the metallic character of

these bonds bulk values for In and Sb are 3.4 ). Allother bonds drawn in Fig. 5 represent covalentlike bondssince the corresponding atomic distances ranging from2.75 to 2.88 differ from the covalent In-Sb bondlength (2.84 ) by less than 2.2%.

The solid line in Fig. 6 represents the calculated (00l) rodbased on our model. The agreement with the measured in-tensities is qualitatively very good: the scattering intensity inthe vicinity of the weak 002 bulk reflection is larger thanthe intensity calculated for a truncated bulk crystal dashedline and the interference effect close to the 002 reflectionis correctly reproduced. Note that 002 is a very weak bulkreflection, since the scattering from the In and Sb sublatticesin the zinc-blende structure almost cancels. Hence the (00l)rod in the vicinity of 002 almost corresponds to an an-tiphase condition with high surface sensitivity. The missing-dimer model of John et al.6 dotted line in Fig. 6 has lessintensity than the truncated crystal. The difference can beexplained by the relative In coverage in the top double layer:our model has nominally 16 In atoms, whereas the missing-dimer model has a reduced In coverage of only 12 In atoms.

Within the In2-In3 chain an additional site In2d with areduced occupancy appeared in some of the direct methodsmaps and could be confirmed by the least-squares refine-ments. For the InSb data set this site is of minor importance

(28% occupancy in contrast to 72% for the In2 site and100% for In3, whereas in the GaAs structure it is dominant(63%). The competing sites 2 and 3 are absent in GaAs. Thisleads to the conclusion that group-III dimerization in the toplayer is favored in GaAs, the lighter compound, and reducedin the heavier compounds. Site 1 in the second chain redarrow is nearly unoccupied in GaAs (19%), in contrast to57% in InSb. These reduced occupancies are consistent withSTM images. Figure 9 shows a filled-state STM image re-corded from the GaAs surface with a bias voltage of3.0 V. The similarity to the simulated STM image shownby Lee et al. calculated for 1.5 V, see the lower left ofFig. 3 in Ref. 18 is striking and indicates that the brightdouble rows correspond to the As atoms on sites 6 in the

row marked by the green arrow in Fig. 5, i.e., the rows in-completely occupied by Ga surface dimers on site 2d. Thedark rows correspond to the rows marked by the red arrow inFig. 5, where according to our structural refinement a smallfraction of the sites 1 is occupied by Ga. However, at somelocations marked with white arrows in Fig. 9 bright spots canbe seen within the black rows indicating disorder in thesite-1 chain which might be caused by this site being occu-pied. Although Ga-derived electronic states are probably notimaged at negative sample bias, the contrast visible in Fig. 9is in agreement with our model of the GaAs(001)-c(82)surface. Reports of disorder caused by partial occupation ofsome sites exist in the literature, e.g., Fig. 4 of Ref. 14. In theInAs structure the In1 chain red arrow in Fig. 5 exhibits a

very high degree of disorder, causing diffuse eighth-orderreflections.

Our model is consistent with the PES data6 which indi-cated that there is a single In surface electronic state. Thestructure is also consistent with early ion scattering measure-ments that show strong evidence of intermixing of group-IIIand group-V elements in the surface layer.27

V. SUMMARY

We have found a unique model for the c(82) recon-struction of the group-III-rich 001 surfaces of three differ-

FIG. 8. Difference plot for the InAs data set using a model withonly Nb atoms (Z41) for the uppermost bilayer. Atomic sitesoccupied by In atoms (Z49) appear as positive peaks solid con-tour lines, and those occupied by As atoms (Z33) as negativepeaks dotted contour lines. Crosses mark the positions of theatomic sites. FIG. 9. Filled-state STM image (3.0 V) recorded from a

GaAs001 surface. White arrows mark disorder in the site-1 chainarising from the reduced occupancy of site 1.


075307-9

8/8/2019 01_PRB_Kumpf

10/10

ent III-V semiconductors GaAs, InAs, and InSb using di-rect methods and subsequent least-squares refinement ofSXRD data. It is supported by density-functional-theory cal-culations, LEED measurements, and simulated STMimages.18 The reconstruction consists of subsurface dimersof group-III elements in the second bilayer and linear chainsof atoms on nonbulklike sites at the surface along the110bulk direction. Within these chains a tendency to dimer

formation exists, which decreases with increasing atomicweight of the compounds. We propose that the model de-scribes all metal-rich III-V surfaces.

ACKNOWLEDGMENTS

We thank the HASYLAB staff for technical assistance.This work was supported by the National Science Founda-tion with Grant No. DMR09705081 L.D.M., the DanishResearch Council through Dansync, the German Bundesmin-isterium fur Bildung, Forschung und Technologie BMBFProject No. 05 KS1GUC/3, the Deutsche Forschungsge-meinschaft Graduiertenkolleg Physik nanostrukturierter

Festkorper, and the IHP program Access to Research In-frastructures of the European Commission Grant No.HPRI-CT-1999-00040.

*Corresponding author. Present address: Lehrstuhl fur Experimen-telle Physik II der Universitat Wurzburg, Am Hubland,D-97074 Wurzburg, Germany. FAX:49 0931 888 5158. Emailaddress: [email protected]

Present address: Cornell High Energy Synchrotron SourceCHESS, Wilson Laboratory, Cornell University, IthacaNY 14853.

Present address: Saab AB, Future Products & Technology, Dept.

FKC-EL, S-58188 Linkoping, Sweden.1 C.F. McConville, T.S. Jones, F.M. Leibsle, S.M. Driver, T.C.Q.Noakes, M.O. Schweitzer, and N.V. Richardson, Phys. Rev. B50, 14 965 1994.

2 M. Gothelid, Y. Garreau, M. Sauvage-Simkin, R. Pinchaux, A.Cricenti, and G. LeLay, Phys. Rev. B 59, 15 285 1999.

3 C. Ratsch, W. Barvosa-Carter, F. Grosse, J.H.G. Owen, and J.J.Zinck, Phys. Rev. B 62, R7719 2000.

4 V.P. LaBella, H. Yang, D.W. Bullock, P.M. Thibado, P. Kratzer,and M. Scheffler, Phys. Rev. Lett. 83, 2989 1999.

5 C. B. Duke, in Physical Structure, Vol. 1 ofHandbook of SurfaceScience, edited by W.N. Unertl Elsevier North-Holland, Am-sterdam, 1996, Chap 6.

6

P. John, T. Miller, and T.-C. Chiang, Phys. Rev. B 39, 17301989.7 J. Cerda, F.J. Palomares, and F. Soria, Phys. Rev. Lett. 75, 665

1995.8 P.R. Varekamp, M. Bjorkqvist, M. Gothelid, and U.O. Karlsson,

Surf. Sci. 350, L221 1996.9 D.K. Biegelsen, R.D. Bringans, J.E. Northrup, and L.-E. Swartz,

Phys. Rev. B 41, 5701 1990.10 Q. Xue, T. Hashizume, J.M. Zhou, T. Sakata, T. Ohno, and T.

Sakurai, Phys. Rev. Lett. 74, 3177 1995.11J.E. Northrup and S. Froyen, Phys. Rev. Lett. 71, 2276 1993.12 S. Ohkouchi and N. Ikoma, Jpn. J. Appl. Phys., Part 1 33, 3710

1994.13 C. Kendrick, G. Le Lay, and A. Kahn, Phys. Rev. B 54, 17 877

1996.14 M.O. Schweitzer, F.M. Leibsle, T.S. Jones, C.F. McConville, and

N.V. Richardson, Surf. Sci. 280, 63 1993.15 A.A. Davis, R.G. Jones, G. Falkenberg, L. Seehofer, R.L.

Johnson, and C.F. McConville, Appl. Phys. Lett. 75, 19381999.

16 S.L. Skala, J.S. Hubacek, J.R. Tucker, J.W. Lyding, S.T. Chou,

and K.-Y. Cheng, Phys. Rev. B 48, 9138 1993.17 N. Jones, C. Norris, C.L. Nicklin, P. Steadman, S.H. Baker, A.D.

Johnson, and S.L. Bennett, Surf. Sci. 409, 27 1998.18 S.-H. Lee, W. Moritz, and M. Scheffler, Phys. Rev. Lett. 85, 3890

2000.19 C. Kumpf, L.D. Marks, D. Ellis, D. Smilgies, E. Landemark, M.

Nielsen, R. Feidenhansl, J. Zegenhagen, O. Bunk, J.H. Zeysing,Y. Su, and R.L. Johnson, Phys. Rev. Lett. 86, 3586 2001.

20 For example, G. Giacovazzo, Direct Methods in CrystallographyPlenum Press, New York, 1980; G. Bricogne, Acta Crystal-logr., Sect. A: Found. Crystallogr. 40, 410 1984; M.M. Wool-fson, ibid. 43, 593 1987; G.M. Sheldrick, ibid. 46, 467 1990;M.M. Woolfson and H. Fan, Physical and Nonphysical Methodsof Solving Crystal Structures Cambridge University Press,Cambridge, 1995; C.J. Gilmore, Acta Crystallogr., Sect. A:Found. Crystallogr. 52, 561 1996.

21 C.J. Gilmore, L.D. Marks, D. Grozea, C. Collazo, E. Landree, andR.D. Twesten, Surf. Sci. 381, 77 1997; C. Collazo-Davila, L.D.Marks, K. Nishii, and Y. Tanishiro, Surf. Rev. Lett. 4, 65 1997;E. Landree, C. Collazo-Davila, and L.D. Marks, Acta Crystal-logr., Sect. B: Struct. Sci. 53, 916 1997; L.D. Marks and E.Landree, Acta Crystallogr., Sect. A: Found. Crystallogr. 54, 2961998; C. Collazo-Davila, D. Grozea, and L.D. Marks, Phys.Rev. Lett. 80, 1678 1998; X. Torrelles, J. Rius, F. Boscherini,S. Heun, B.H. Mueller, S. Ferrer, J. Alvarez, and C. Miravitlles,Phys. Rev. B 57, R4281 1998.

22 For example, L.G. Gubin, B.T. Polyak, and E.V. Raik, USSRComput. Math. Math. Phys. 7, 1 1967; D.C. Youla, in Image

Recovery, Theory and Application, edited by H. Stark Aca-demic Press, Orlando, 1987; M.H. Hayes, ibid.; A. Levi and H.Stark, ibid.; P.L. Combettes, Adv. Imaging Electron Phys. 95,155 1996.

23 L.D. Marks, W. Sinkler, and E. Landree, Acta Crystallogr., Sect.A: Found. Crystallogr. 55, 601 1999.

24 L.D. Marks, Phys. Rev. B 60, 2771 1999.25 U. Resch-Esser, N. Esser, D.T. Wang, M. Kuball, J. Zegenhagen,

B.O. Fimland, and W. Richter, Surf. Sci. 352-354, 71 1996.26 R. Feidenhansl, Surf. Sci. Rep. 10, 105 1989; E. Vlieg, J. Appl.

Crystallogr. 30, 532 1997.27 J. Falta, R.M. Tromp, M. Copel, G.D. Pettit, and P.D. Kirchner,

Phys. Rev. Lett. 69, 3068 1992.


075307-10

Documents

01_PRB_Kumpf